Bayesian Analysis of Stochastically Ordered Distributions of Categorical Variables

Abstract

This article considers a finite set of discrete distributions all having the same finite support. The problem of interest is to assess the strength of evidence produced by sampled data for a hypothesis of a specified stochastic ordering among the underlying distributions and to estimate these distributions subject to the ordering. We present a Bayesian approach that is an alternative to using the posterior probability of the hypothesis and the Bayes factor in favor of the hypothesis. We develop computational methods for the implementation of Bayesian analyses. We analyze examples to illustrate inferential and computational developments. The methodology used for testing a hypothesis is seen to apply to a wide class of problems in Bayesian inference and has some distinct advantages.